Non-transitory computer-readable medium and method for monitoring a semiconductor fabrication process

ABSTRACT

A non-transitory computer-readable medium for monitoring a semiconductor fabrication process includes an image conversion model having an artificial neural network. The image conversion model, when executed, causes the processor to receive a first image and a second image of a semiconductor wafer. The artificial neural network is trained by inputting a dataset representing the first image and the second image, generating a conversion image of the semiconductor wafer and calibrating weights and biases of the artificial neural network to match the conversion image to the second image. A third image of the semiconductor wafer is generated based on the calibrated weights and biases of the artificial neural network. The image conversion model with the trained artificial neural network may be transmitted to another device for image conversion of low resolution images.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. § 119 to Korean PatentApplication No. 10-2018-0109500, filed on Sep. 13, 2018 in the KoreanIntellectual Property Office, the disclosure of which is incorporated byreference herein in its entirety.

1. Technical Field

Embodiments of the inventive concept described herein relate to anon-transitory computer-readable medium including an image conversionmodel having an artificial neural network and a method of converting animage of a semiconductor wafer, for monitoring a semiconductorfabrication process.

2. Discussion of Related Art

Developments in miniaturizing the process of manufacturing asemiconductor device have resulted in the shrinking of a design rule anda decrease in a critical dimension (CD). Therefore, it is necessary toaccurately monitor a fabrication process of a semiconductor device.

An electron microscope such as a critical dimension scanning electronmicroscope (CD-SEM) may be used to monitor the fabrication process of asemiconductor device. For monitoring shrinking materials and dimensions,the size of an electron beam output from the electron microscope has tobe reduced, along with improved electronic detectors. To obtain ahigh-resolution image from the electron microscope, more time andprocessing resources are needed. For example, scanning a field of view(FOV) area with more frames, and more iterations of processing arerequired to improve signal to noise ratio (SNR). In this case, a timenecessary to obtain the high-resolution image may increase. The increasein the time necessary to obtain the high-resolution image from theelectron microscope may cause an increase in a time necessary tofabricate a semiconductor device or an increase in the number ofelectron microscopes used to improve the above-described time. In anycase, an increase in a time and costs necessary to monitor asemiconductor fabrication process is inevitable.

SUMMARY

Embodiments of the inventive concept provide a non-transitorycomputer-readable medium including an image conversion model whichincludes an artificial neural network and a method of converting animage of a semiconductor wafer for monitoring a semiconductorfabrication process.

According to an exemplary embodiment, a non-transitory computer-readablemedium for monitoring a semiconductor fabrication process includes animage conversion model stored on the non-transitory computer-readablemedium. The image conversion model includes an artificial neuralnetwork. The image conversion model includes instructions executable byat least one processor, the instructions when executed by the at leastone processor, causes the processor to receive a first image and asecond image of a semiconductor wafer, the first image and the secondimage being generated by a measuring device, wherein the second imagehas a higher resolution than the first image. The artificial neuralnetwork is trained by inputting a dataset representing the first imageand the second image; generating a conversion image of the semiconductorwafer based on the first image, the conversion image having a higherresolution than the first image; and calibrating weights and biases ofthe artificial neural network to match the conversion image to thesecond image within a predetermined differential reference value. Athird image of the semiconductor wafer is generated based on thecalibrated weights and biases of the artificial neural network.

According to an exemplary embodiment, a method of converting an image ofa semiconductor wafer to monitor a semiconductor fabrication processincludes receiving a first image and a second image of a semiconductorwafer by a processor executing an image conversion model having anartificial neural network. The artificial neural network of the imageconversion model is trained by: inputting a dataset representing thefirst image and the second image; generating a conversion image of thesemiconductor wafer based on the first image, the conversion imagehaving a higher resolution than the first image; and calibrating weightsand biases of the artificial neural network to match the conversionimage to the second image within a predetermined differential referencevalue. A third image is generated based on the calibrated weights andbiases of the artificial neural network.

According to an exemplary embodiment, a system includes at least oneprocessor; and at least one non-transitory computer-readable storagemedium storing instructions that, when executed by the at least oneprocessor, cause the system to receive a first image and a second imageof a semiconductor wafer, the first image and the second image beinggenerated by a measuring device, wherein the second image has a higherresolution than the first image. An artificial neural network of animage conversion model is trained by: inputting a dataset representingthe first image and the second image; generating a conversion image ofthe semiconductor wafer based on the first image, the conversion imagehaving a higher resolution than the first image; and calibrating weightsand biases of the artificial neural network to match the conversionimage to the second image within a predetermined differential referencevalue. A third image of the semiconductor wafer is generated based onthe calibrated weights and biases of the artificial neural network.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a diagram illustrating a system for monitoring a semiconductorfabrication process according to an exemplary embodiment of theinventive concept.

FIG. 2 is a diagram illustrating a process in which the artificialneural network of the image conversion model is trained based on animage pair of FIG. 1 according to an exemplary embodiment of theinventive concept.

FIG. 3 is a diagram illustrating an artificial neural network of theimage conversion model according to an exemplary embodiment of theinventive concept.

FIG. 4 is a flowchart illustrating sub operations of operation S150 ofFIG. 2 according to an exemplary embodiment of the inventive concept.

FIGS. 5 to 7 are diagrams illustrating a low-resolution image, ahigh-resolution image and a conversion image of a semiconductor waferaccording to an exemplary embodiment of the inventive concept.

FIG. 8 is a graph showing a comparison between a low-resolution image, ahigh-resolution image and a conversion image of FIGS. 5 to 7 accordingto an exemplary embodiment of the inventive concept.

FIG. 9 is a diagram illustrating a process in which a system of FIG. 1monitors a semiconductor wafer according to an exemplary embodiment ofthe inventive concept.

FIG. 10 is a diagram illustrating a process in which a system of FIG. 9monitors a semiconductor wafer according to an exemplary embodiment ofthe inventive concept.

FIG. 11 is a diagram illustrating a system for monitoring asemiconductor fabrication process according to another exemplaryembodiment of the inventive concept.

FIG. 12 is a diagram illustrating a system for monitoring asemiconductor fabrication process according to another exemplaryembodiment of the inventive concept.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Below, exemplary embodiments of the inventive concept will be describedin detail and clearly to such an extent that one of ordinary skill inthe art may easily implement the inventive concept.

FIG. 1 is a diagram illustrating a system for monitoring a semiconductorfabrication process according to an exemplary embodiment of theinventive concept. A system 100 may include a measuring device 110, afirst computer 120 and a second computer 130. The system 100 may beconfigured to monitor a fabrication process of various semiconductordevices. For example, the fabrication process may include a process inwhich any semiconductor device is fabricated on a semiconductor wafer, aprocess in which a semiconductor device implemented on the semiconductorwafer is packaged or tested, etc.

A semiconductor device which is monitored by the system 100 may include,for example, a memory device, such as a dynamic random access memory(DRAM) device, a static random access memory (SRAM) device, a thyristorrandom access memory (TRAM) device, a NAND flash memory device, a NORflash memory device, a resistive random access memory (RRAM) device, aferroelectric random access memory (FRAM) device, a phase change randomaccess memory (PRAM) device, a magnetic random access memory (MRAM)device, a dual in-line memory module (DIMM), a solid state drive (SSD)or a memory card. The semiconductor device which is monitored by thesystem may also include a processing device, such as a centralprocessing unit (CPU), an image signal processing unit (ISP), a digitalsignal processing unit (DSP), a graphics processing unit (GPU), a visionprocessing unit (VPU) or a neural processing unit (NPU). Thesemiconductor device which is monitored by the system may also include asystem on chip (SoC), an application specific integrated circuit (ASIC),a field-programmable gate array (FPGA), etc. In the exemplary embodimentdescribed below, the semiconductor device is a semiconductor wafer, butthe inventive concept is not limited thereto.

The system may include a measuring device 110. The measuring device 110may be an electron microscope which is used to monitor a fabricationprocess for semiconductor wafers including a first semiconductor waferWF1. For example, the electron microscope may be critical dimensionscanning electron microscopy (CI)-SEM) equipment, a critical dimensionscanning electron microscope (CD-SEM), a cross-sectional SEM or atransmission electron microscope (TEM).

The measuring device 110 may be configured to measure or monitor a firstsemiconductor wafer WF1. The measuring device 110 may be configured togenerate an image of the first semiconductor wafer WF1. The image of thefirst semiconductor wafer WF1 generated by the measuring device 110 maybe used to measure a structure of the first semiconductor wafer WF1 orto determine a defect of the first semiconductor wafer WF1. For example,referring to FIG. 1, relatively dark portions of the images may indicateholes that are penetrating the first semiconductor wafer WF1. However,the images shown in FIG. 1 are only exemplary.

In one exemplary embodiment, the measuring device 110 may include anelectron gun which emits or radiates an electron beam to the firstsemiconductor wafer WF1. The measuring device 110 may also include adetector which detects electrons generated from the first semiconductorwafer WF1. The measuring device 110 may also include a processor whichprocesses the detected electrons and generates an image of the firstsemiconductor wafer WF1. The processor may also be configured to controlthe electron gun and the detector. The measuring device 110 may alsoinclude a memory device which is configured to store images, includingthe image of the first semiconductor wafer WF1.

In an embodiment, the measuring device 110 may be configured tophotograph the same point or location of the first semiconductor waferWF1 and may generate an image pair that includes a low-resolution image(e.g., 512×512) and at least one high-resolution image (e.g.,1024×1024). The numerical values of pixels of the above low-resolutionand high-resolution images are only exemplary. Furthermore, while theexemplary embodiment describes a single low-resolution andhigh-resolution image for the image pair, in other embodiments, themeasuring device 110 may generate a plurality of low-resolution imagesand high-resolution images for the image pair. The measuring device 110may be configured to transmit or provide the image pair to a firstcomputer 120.

In one exemplary embodiment, the low-resolution image and thehigh-resolution image may be captured at the same location of the firstsemiconductor wafer WF1. The high-resolution image and thelow-resolution image may be also referred to as a “high-quality image”and a “low-quality image”, respectively. The amount of information ofthe first semiconductor wafer WF1 included in the high-resolution imagemay be greater than the amount of information of the first semiconductorwafer WF1 included in the low-resolution image. As a critical dimension(CD) of the first semiconductor wafer WF1 decreases, it may be moreaccurate to measure or test the first semiconductor wafer WF1 using thehigh-resolution image rather than the low-resolution image.

The first computer 120 may receive the image pair from the measuringdevice 110 and may transmit or provide the image pair to a secondcomputer 130 without modification. Alternatively, the first computer 120may process the received image pair and may transmit or provide theprocessed image pair to the second computer 130.

The first computer 120 may include a first processor 121 and a firstmemory device 122. The first processor 121 may be any one of theprocessing devices described above. The first memory device 122 may beany one of the memory devices described above. In other exemplaryembodiments, the first computer 120 may include one or more firstprocessors 121 and one or more first memory devices 122. The firstcomputer 120 may include homogeneous or heterogeneous processors andhomogeneous or heterogeneous memory devices. The first processor 121 mayprocess the image pair and may store the processed image pair to thefirst memory device 122.

In another exemplary embodiment, the system 100 may include a pluralityof measuring devices 110. The first computer 120 may be a server whichmay control or manage the plurality of measuring devices 110 and mayreceive image pairs from the respective measuring devices 110. In otherexemplary embodiments, the system 100 may include a plurality of firstcomputers 120 communicating with the plurality of measuring devices 110.

The second computer 130 may be configured to receive the image pair fromthe first computer 120. The second computer 130 includes “an imageconversion model” 123 or an “image converter” which includes anartificial neural network. The image conversion model 123 includesinstructions for training the artificial neural network. The imageconversion model 123 having a trained artificial neural network mayconvert a low resolution image to a high resolution image. The imageconversion model 123 may be configured to train the artificial neuralnetwork by inputting a dataset representing the first and second imagesof the image pair and calibrating weights and biases of the artificialneural network. In one exemplary embodiment, after the artificial neuralnetwork of the image conversion model 123 is trained, the secondcomputer 130 may be configured to transmit or provide the imageconversion model 123 which includes the trained artificial neuralnetwork to the first computer 120.

The artificial neural network of the image conversion model 123 mayinclude a plurality of neurons. In one exemplary embodiment, theartificial neural network may be a convolutional neural network (CNN) ora super resolution convolutional neural network (SRCNN).

The second computer 130 may be configured to execute the imageconversion model 123 which includes the artificial neural network andmay convert a low-resolution image to a high-resolution image. In oneexemplary embodiment, the second computer 130 may be a deep learningserver which is specialized to execute the image conversion model 123.In the exemplary embodiment shown in FIG. 1, the system 100 includes onesecond computer 130. However, in other exemplary embodiments, the systemmay include a plurality of second computers 130. In other exemplaryembodiments, the first 120 and second 130 computers may be performed bya single computer having one or more processors or GPUs.

In one exemplary embodiment, the second computer 130 may include asecond processor 131 and a second memory device 132. The secondprocessor 131 may be any one of the processing devices described above.The second memory device 132 may be any one of the memory devicesdescribed above. In certain exemplary embodiments, the second computer130 may include one or more second processors 131 and one or more secondmemory devices 132. The second computer 130 may include homogeneous orheterogeneous processors and homogeneous or heterogeneous memorydevices.

The image conversion model 123 may be executed by the at least onesecond processor 131. The weights and biases of the artificial neuralnetwork of the image conversion model 123 are stored in the at least onesecond memory device. The second memory device 132 may be a storagemedium which stores information about the artificial neural network. Theartificial neural network may be implemented by software or hardware,such as logic circuits, or a combination of hardware and software.

Costs and a time necessary to generate a high-resolution image may begreater than costs and a time necessary to generate a low-resolutionimage. Accordingly, in an exemplary embodiment of the inventive concept,a low-resolution image may be converted to a high-resolution image bythe image conversion model 123. For example, in one exemplaryembodiment, the first semiconductor wafer WF1 may be a samplesemiconductor wafer and the image pair of the first semiconductor waferWF1 may be a sample image pair. As shown in FIGS. 1-2, the system 100includes the image conversion model 123 which is configured to train theartificial neural network by calibrating the weights and biases based ona comparison of the images of the sample image pair. After theartificial neural network of the image conversion model 123 is trained,the image conversion model 123 may convert a low-resolution image of anyother semiconductor wafer to a high-resolution image. Accordingly, theimage conversion model 123 may obviate the need for the measuring device110 to generate a high-resolution image associated with the othersemiconductor wafers. Therefore, both the time and costs required toobtain a high-resolution image of a semiconductor wafer may be improvedby the image conversion model 123. The processes in which the artificialneural network of the image conversion model 123 is trained and the useof the trained artificial neural network of the image conversion model123 will be described with reference to FIGS. 2 to 8.

FIG. 2 is a diagram illustrating a process in which the artificialneural network of the image conversion model is trained based on thedataset from the image pair of FIG. 1. FIG. 2 will be described withreference to FIG. 1.

In operation S110, the measuring device 110 may monitor or measure thefirst semiconductor wafer WF1 and may generate at least onelow-resolution image and at least one high-resolution image of the firstsemiconductor wafer WF1. In an exemplary embodiment, the firstsemiconductor wafer WF1 may be any one of a plurality of semiconductorwafers manufactured through a semiconductor fabrication process that isselected as a sample semiconductor wafer. Since it is necessary toincrease the number of measurement frames or a resolution of themeasuring device 110 for measuring the high-resolution image, a timenecessary for the measuring device 110 to scan the first semiconductorwafer WF1 or the number of times to scan the first semiconductor waferWF1 may increase. Accordingly, a time necessary for the measuring device110 to generate the high-resolution image may be longer than a timenecessary for the measuring device 110 to generate the low-resolutionimage.

In one exemplary embodiment, the measuring device 110 may generate asecond image pair of a low-resolution image and a high-resolution imageindicating a second location of the first semiconductor wafer WF1. Thesecond image pair is in addition to a first image pair of alow-resolution image and a high-resolution image indicating a firstlocation of the first semiconductor wafer WF1. As the number of imagepairs respectively indicating a plurality of locations of the firstsemiconductor wafer WF1 is increased by the measuring device 110, thecalibration (or accuracy) of the weights and biases of the artificialneural network of the image conversion model 123 by the second computer130 may be improved. Also, as various shapes or features of the firstsemiconductor wafer WF1 are included in the image pairs, the accuracy ofthe calibration of the weights and biases of the artificial neuralnetwork of the image conversion model 123 may be improved. The measuringdevice 110 may be configured to generate a plurality of image pairsindicating a plurality of locations of the first semiconductor waferWF1.

In operation S120, the measuring device 110 may transmit at least oneimage pair to the first computer 120. The measuring device 110 and thefirst computer 120 may communicate with each other through a physical orlogical network such as an Internet, an intranet, a local area network(LAN), a wide area network (WAN), etc. Each of the measuring device 110and the first computer 120 may support wired communication or wirelesscommunication.

In operation S130, the first computer 120 may receive the at least oneimage pair. For example, an offset may exist between the low-resolutionimage and the high-resolution image generated in operation S110. Thefirst processor 121 of the first computer 120 may be configured tocorrect or calibrate the offset between the low-resolution image and thehigh-resolution image. For example, in one exemplary embodiment, tocorrect the offset, the first processor 121 may perform Fouriertransform on the low-resolution image and the high-resolution image toadjust a phase difference, and thus, locations of the images may beadjusted. For another example, to correct the offset, the firstprocessor 121 may allow the low-resolution image and the high-resolutionimage to overlap each other and may adjust locations of the images sothat an overlapping result is maximally clear.

In operation S140, the first computer 120 may be configured to transmitthe offset-corrected image pair to the second computer 130. The firstcomputer 120 and the second computer 130 may communicate with each otherthrough the above-described physical or logical network. The secondcomputer 130 may support wired communication or wireless communication.However, in alternative embodiments, the first computer 120 may receivean image pair and may not correct an offset between a low-resolutionimage and a high-resolution image. In this embodiment, the firstcomputer 120 may transmit the received image pair to the second computer130 without modification.

In operations S150-S180, the second processor 131 of the second computer130 executing the image conversion model 123 may train the artificialneural network by inputting the dataset represented by the image pairinto the artificial neural network and calibrating the weights andbiases of the artificial neural network. The weights and biases of theartificial neural network are calibrated until a conversion imagegenerated by the image conversion model 123 based on the low-resolutionimage is sufficiently similar to the high-resolution image. A resolutionof the conversion image converted by the image conversion model 123 maybe higher than a resolution of the low-resolution image. A timenecessary for the conversion of a low-resolution image by the imageconversion model 123 executed by the second processor 131 may be veryshorter than a time necessary for the generation of a high-resolutionimage by the measuring device 110.

In Operation S150, the image conversion model 123 generates a conversionimage based on the low-resolution image. Operation S150 will be morefully described with reference to FIGS. 3 and 4. In operation S160, thesecond processor 131 may compare the conversion image of operation S150with the high-resolution image of operation S110. Since thehigh-resolution image of operation S110 is compared with the conversionimage, the high-resolution image may be referred to as a “referenceimage”. For example, in one exemplary embodiment, the second processor131 may be configured to calculate a mean square error (MSE) as a lossfunction “L” for a difference between the conversion image and thehigh-resolution image. The loss function “L” may be expressed byEquation 1.

$\begin{matrix}{{L\left( {W,B} \right)} = {\frac{1}{n}{\sum\limits_{1}^{n}\;{{{C\left( {W,B} \right)} - H}}^{2}}}} & \left\lbrack {{Equation}\mspace{14mu} 1} \right\rbrack\end{matrix}$

“W” may indicate weights of an artificial neural network, “B” mayindicate biases of the artificial neural network, “C” may indicate anoutput of the artificial neural network (e.g., the conversion image),and “H” may indicate the high-resolution image generated in operationS110. “n” may indicate the number of sample images input to theartificial neural network for training, such as the number of imagepairs generated in operation S110. For example, the loss function “L”may be calculated based on a pixel unit of the conversion image and thehigh-resolution image.

In operation S170, the second processor 131 may be configured todetermine whether the conversion image is matched with or similar to thehigh-resolution image, based on a result of the comparison. If theconversion image is matched with the high-resolution image or theconversion image is similar to the high-resolution image, this mayindicate that the image conversion model 123 is sufficiently accurate.In this case, the second processor 131 may perform operation S190 andtransmit the image conversion model 123 with the trained artificialneural network to the first computer 120. However, if the conversionimage is not matched with the high-resolution image or the conversionimage is not similar to the high-resolution image, this may indicatethat calibration of the artificial neural network is required. In thiscase, the second processor 131 may be configured to perform operationS180 and calibrate the weights and biases of the artificial neuralnetwork. For example, the second processor 131 may determine whether avalue of the loss function “L” is minimized or compare L to a referencevalue.

In operation S180, the second processor 131 executing the imageconversion model 123 may be configured to calibrate information of theartificial neural network so that the conversion image of operation S150is matched with the high-resolution image of operation S110. In oneexemplary embodiment, the second processor 131 is configured tocalibrate the weights and biases of the artificial neural network. Inone exemplary embodiment, the second processor 131 may be configured touse the comparison result (e.g., the value of the loss function “L”) ofoperation S160 to correct the weights and the biases. The secondprocessor 131 may be configured to repeat operation S150 to operationS180 until the image conversion model 123 is sufficiently accurate.

The second processor 131 executing the image conversion model 123 may beconfigured to compare the conversion image with the high-resolutionimage, calibrate the weights and biases of the artificial neural networkof the image conversion model 123 based on a result of the comparison,and again convert the low-resolution image by using the artificialneural network having the calibrated weights and biases. The secondprocessor 131 may be configured to repeatedly perform operation S150 tooperation S180 until the conversion image is matched with thehigh-resolution image or the conversion image becomes similar to thehigh-resolution image. For example, the second processor 131 may beconfigured to repeatedly perform operation S150 to operation S180 untilthe value of the loss function “L” is minimized or is smaller than areference value. Through operation S150 to operation S180 (e.g.,training) repeatedly performed by the second processor 131 executing theimage conversion model 123, the artificial neural network of the imageconversion model 123 may be trained so that the image conversion model123 may convert any low-resolution image to a high-resolution image. Theimage pair generated in operation S110 may be utilized for the trainingof the artificial neural network of the image conversion model 123 andmay be referred to as a “training set”.

The second processor 131 may be configured to store or update theweights and biases calibrated through operation S150 to operation S180in the second memory device 132. Additionally, the second processor 131may repeatedly store or update the value of the loss function “L” in thesecond memory device 132.

The second memory device 132 may be a non-transitory computer-readablemedium storing or including the image conversion model 123. The weightsand biases of the artificial neural network of the image conversionmodel 123 in the second memory device 132 may be updated and optimizedby the second processor 131 until the conversion image generated by theimage converter is matched with the high-resolution image or theconversion image becomes similar to the high-resolution image.

In operation S190, the second processor 131 may be configured totransmit, provide, or output the image conversion model 123 whichincludes the trained artificial neural network to the first computer120. The image conversion model 123 may be stored in the first memorydevice 122 of the first computer 120. After the first computer 120receives the image conversion model 123 having the trained artificialneural network in operation S190, the first processor 121 may beconfigured to convert a low-resolution image to a high-resolution image(e.g., a conversion image) by using the image conversion model 123.

FIG. 3 is a diagram illustrating an artificial neural network 133 whichis executed on a second computer of FIG. 1. FIG. 4 is a flowchartillustrating sub operations of operation S150 of FIG. 2. FIGS. 3 and 4will be described with reference to FIGS. 1 and 2 together.

An artificial neural network 133 which is executed by the secondprocessor 131 may include a first layer 133_1, a second layer 133_2, anda third layer 133_3. In an exemplary embodiment, the artificial neuralnetwork 133 may include at least one or more layers. As the number oflayers increases, a depth of the artificial neural network 133 mayincrease. Each of the first to third layers 133_1 to 133_3 may include aplurality of neurons. A neuron may be configured to receive a resultobtained by adding biases to a result of multiplying input signals andweights together and may output a signal to another neuron. The inputsignals may be provided from any other neurons or may be provided fromthe low-resolution image of operation S110.

In operation S151, the second processor 131 executing the imageconversion model may provide the low-resolution image to the first layer133_1. The second processor 131 executing the image conversion model maygenerate a first feature map data F₁(I) associated with thelow-resolution image based on first weights W₁ and first biases B₁ ofthe first layers 133_1. The operation of the first layer 133_1 may beexpressed by Equation 2.F ₁(I)=max(0,W ₁ *I+B ₁)  [Equation 2]

“I” may indicate an input image, such as a low-resolution image. “*” mayindicate a convolution operation. The second processor 131 may beconfigured to perform the operation of the first layer 133_1 and mayextract a patch of the low-resolution image.

The convolution operation of Equation 2 may be repeatedly performedwhile at least one filter smaller in size than the low-resolution imageis sequentially shifted on the low-resolution image. In one exemplaryembodiment, the filter shift may accompany the following operations: 1)data of the low-resolution image corresponding to a location of thefilter and the first weights W₁ may be multiplied together, 2) allmultiplication results may be added, and 3) the first biases B₁ may beadded to the addition results. The second processor 131 may beconfigured to perform a convolution operation associated with the firstweights W₁ and an addition operation associated with the first biasesB₁. The first layer 133_1 may be referred to as a “convolution layer”.

The second processor 131 executing the image conversion model maygenerate the first feature map data F₁(I) by applying an activationfunction to a result of the above-described operations. As shown in theexemplary embodiment of Equation 2, a rectified linear unit (ReLU)function may be applied. However, the second processor 131 may beconfigured to use any other activation function such as a Leaky ReLUfunction, a sigmoid function, a Tan H function, or an ArcTan function.

In operation S152, the first feature map data F₁(I) may be provided tothe second layer 133_2 under control of the second processor 131. Thesecond processor 131 may be configured to nonlinearly map the firstfeature map data F₁(I) onto second feature map data F₂(I) based onsecond weights W₂ and second biases B₂ of the second layer 133_2. Theoperation of the second layer 133_2 may be expressed by Equation 3.F ₂(I)=max(0,W ₂ *F ₁(I)+B ₂)  [Equation 3]

Equation 3 may be similar to Equation 2 except that the first featuremap data F₁(I), the second weights W₂, and the second biases B₂ are usedinstead of the low-resolution image “I”, the first weights W₁, and thefirst biases B₁. The second processor 131 may be configured to performan operation of the second layer 1332 and may generate the secondfeature map data F₂(I). The second processor 131 may be configured toperform a convolution operation associated with the second weights W₂and an addition operation associated with the second biases B₂. Thesecond layer 133_2 may be referred to as a “convolution layer”.

In operation S153, the second processor 131 executing the imageconversion model may be configured to provide the second feature mapdata F₂(I) to the third layer 133_3. The second processor 131 may beconfigured to reconstruct the second feature map data F₂(I) to aconversion image based on third weights W₃ and third biases B₃ of thethird layer 133_3. The operation of the third layer 133_3 may beexpressed by Equation 4.F ₃(I)=W ₃ −F ₂(I)+B ₃  [Equation 4]

Equation 4 may be similar to Equation 3 except that the second featuremap data F₂(I), the third weights W₃ and the third biases B₃ are usedinstead of the first feature map data F₁(I), the second weights W₂ andthe second biases B₂. The second processor 131 may be configured toperform a convolution operation associated with the third weights W₃ andan addition operation associated with the third biases B₃. The thirdlayer 133_3 may be referred to as a “convolution layer”.

The third layer 133_3 may correspond to the last layer of layers in theartificial neural network 133. For example, in one exemplary embodiment,the filter shift may accompany the following operations: 1) a portion ofthe second feature map data F₂(I) corresponding to a location of thefilter and the third weights W₃ may be multiplied together, 2) allmultiplication results may be added, and 3) the third biases B₃ may beadded to the addition results. However, the second processor 131 may beconfigured to refrain from applying an activation function to a resultof the above-described operations. The second processor 131 may performthe operation of the third layer 133_3 and may generate the conversionimage.

As described above, the second processor 131 executing the imageconversion model may be configured to calibrate the weights and biasesof the artificial neural network so that the conversion image generatedthrough operation S151 to operation S153 is matched with thehigh-resolution image (operation S180). The second processor 131 may beconfigured to compare the conversion image with the high-resolutionimage and may calibrate the first to third weights W₁ to W₃ and thefirst to third biases B₁ to B₃ based on a result of the comparison. Thesecond processor 131 executing the image conversion model may beconfigured to repeatedly perform calibration of the weights and biasesof operations S151, S152, S153, S160, S170 and S180. The secondprocessor 131 may then perform operation S151 to operation S153 based onthe calibrated first to third weights W₁ to W₃ and the calibrated firstto third biases B₁ to B₃.

FIGS. 5 to 7 are diagrams illustrating a low-resolution image, ahigh-resolution image and a conversion image of a semiconductor waferaccording to an embodiment of the inventive concept. FIG. 8 is a diagramillustrating a graph for comparison between a low-resolution image, ahigh-resolution image and a conversion image of FIGS. 5 to 7. FIGS. 5 to8 will be described together with reference to FIGS. 1 and 2.

In one exemplary embodiment, an image of FIG. 5 may be a low-resolutionimage of the first semiconductor wafer WF1 generated by the measuringdevice 110 as described in operation S110. In one exemplary embodiment,an image of FIG. 6 may be a high-resolution image of the firstsemiconductor wafer WF1 generated by the measuring device 110 asdescribed in operation S110. An image of FIG. 7 may be a conversionimage generated by the image conversion model with a trained artificialneural network as described in operation S150 to operation S180, whichmay be repeatedly performed. The conversion image of FIG. 7 may have ahigher resolution than the low-resolution image of FIG. 5. Theconversion image of FIG. 7 and the high-resolution image of FIG. 6 maybe matched with each other or may be similar to each other.

In FIG. 8, a horizontal axis may represent a plurality of samplesrepeatedly arranged on the first semiconductor wafer WF1. A sample maybe referred to as a “semiconductor die”, a “semiconductor chip”, a“semiconductor device”, etc. In FIG. 8, a vertical axis may representthe sizes D1, D2, and D3 or diameters of structures (e.g., pillars) onthe images of FIGS. 5 to 8. Referring to FIG. 8, first differences orerrors between the sizes D3 of conversion images, which are generated byconverting low-resolution images corresponding to the plurality ofsamples by the image conversion model and the sizes D2 ofhigh-resolution images may be smaller than second differences or errorsbetween the low-resolution images D1 corresponding to the plurality ofsamples and the sizes D2 of the high-resolution images. An average ofthe second differences may decrease as much as 70% or more by the imageconversion model executed by the second processor 131. For example, inone exemplary embodiment, an average of the first errors may be lessthan 30% of the average of the second differences.

After the artificial neural network of the image conversion model iscompletely trained through operation S110 to operation S180, themeasuring device 110 may generate only a low-resolution image of asemiconductor wafer and the low-resolution image may be converted to aconversion image having a high resolution by the image conversion model.Accordingly, in one exemplary embodiment, the monitoring of themanufacture of a semiconductor device may be performed by the measuringdevice 110 without generating a high-resolution image of thesemiconductor wafer. Since the measuring device 110 does not need togenerate a high-resolution image of a semiconductor wafer, the costs andtime necessary for the measuring device 110 to test the semiconductorwafer may decrease. Additionally, the capacity of the measuring device110 may be improved.

FIG. 9 is a diagram illustrating a process in which a system of FIG. 1monitors a semiconductor wafer. FIG. 9 will be described with referenceto FIGS. 1 and 2.

In one exemplary embodiment, after training of the artificial neuralnetwork is completed by the second processor 131 of the second computer130 according to operation S190 of FIG. 2, the second computer 130 maybe configured to transmit the image conversion model (e.g., the SRCNNmodel) stored in the second memory device 132 to the first computer 120.The first processor 121 may store the image conversion model in thefirst memory device 122. The measuring device 110 may be configured togenerate low-resolution images of a second semiconductor wafer WF2. Thesecond semiconductor wafer WF2 may be a semiconductor wafer which ismanufactured identically to the first semiconductor wafer WF1 but is notselected as a sample semiconductor wafer for the training of theartificial neural network of the image conversion model. In theexemplary embodiment shown in FIG. 9, one second semiconductor wafer WF2is provided to the measuring device 110. However, the number ofsemiconductor wafers to be provided to the measuring device 110 is notlimited to the example illustrated in FIG. 9.

The first processor 121 may be configured to convert the low-resolutionimages of the second semiconductor wafer WF2 and generate conversionimages by using the image conversion model having the trained artificialneural network. The first processor 121 may execute the image conversionmodel without modification, the training of which is completed by thesecond processor 131. The conversion image may be generated by the imageconversion model executed by the first processor 121 instead ofgenerating a high-resolution image of the second semiconductor wafer WF2at the measuring device 110. Accordingly, the time necessary to test ordetermine the second semiconductor wafer WF2 may be decreased.

As illustrated in FIG. 9, the first processor 121 may be configured toprovide the conversion image to the measuring device 110. However, inalternative exemplary embodiments, the first processor 121 may beconfigured to provide the conversion image to any other device and auser may check the conversion image through the other device. Theabove-described storage device may be configured to store the conversionimage and may display the conversion image. In some exemplaryembodiments, the measuring device 110 may also be configured to displaythe conversion image to enable the user to view the conversion image onthe measuring device.

FIG. 10 is a diagram illustrating a process in which a system of FIG. 9monitors a semiconductor wafer. FIG. 10 will be described together withreference to FIGS. 2 and 9.

In operation S210, the measuring device 110 may be configured togenerate a low-resolution image of a second semiconductor wafer. Inoperation S210, the measuring device 110 may be configured to refrainfrom generating a high-resolution image of the second semiconductorwafer. In operation S220, the measuring device 110 may be configured totransmit the low-resolution image to the first computer 120. Forexample, operation S220 may be performed only after the image conversionmodel having the trained artificial neural network is transferred to thefirst computer 120 in operation S190.

In operation S230, the first processor 121 of the first computer 120 maybe configured to convert the transmitted low-resolution image by usingthe image conversion model. The first memory device 122 may be anon-transitory computer-readable medium storing or including the imageconversion model.

The artificial neural network of the image conversion model executed bythe first computer 120 may be trained by the second processor 131 basedon the sample images of operation S110 as shown in FIG. 2. The imageconversion model which includes the trained artificial neural networkmay be continuously used to convert a low-resolution image to aconversion image having a high resolution. The first computer 120 maytransmit the conversion image to the measuring device 110. As describedabove, the measuring device 110 may be configured to refrain fromgenerating a high-resolution image after operation S190 of FIG. 2. Thehigh-resolution image may be generated by the first processor executingthe image conversion model instead of the measuring device 110. Thefirst computer 120 may be configured to repeatedly perform operationS210 to operation S230 as semiconductor wafers are provided to themeasuring device 110.

In operation S310, the measuring device 110 may monitor a samplesemiconductor wafer and may generate a low-resolution image and ahigh-resolution image of the sample semiconductor wafer. The samplesemiconductor wafer of operation S310 may be any one of a plurality ofsemiconductor wafers manufactured through the semiconductor fabricationprocess. In one exemplary embodiment, the sample semiconductor wafer ofoperation S310 may be different from the first semiconductor wafer WF1of operation S110.

The measuring device 110 may be configured to perform operation S310periodically or randomly to check and maintain the accuracy andconsistency of the image conversion model. For example, the measuringdevice 110 may perform operation S310 at specific temporal periods. Inanother exemplary embodiment, the measuring device 110 may performoperation S310 in response to a request of the user. In one exemplaryembodiment, operation S310 may be similar to operation S10. In anotherexemplary embodiment, the measuring device 110 may be configured toperform operation S310 when the measuring device measures a new color, anew structure, or a new pattern of a semiconductor wafer or the type ofsemiconductor wafer is changed.

In operation S320, the measuring device 110 may be configured totransmit only the low-resolution image to the first computer 120. Inoperation S330, the first computer 120 may be configured to convert thetransmitted low-resolution image by using the image conversion modelwhich includes the trained artificial neural network. The first computer120 may be configured to transmit the conversion image having the higherresolution than the low-resolution image to the measuring device 110. Inone exemplary embodiment, operation S320 and operation S330 are similarto operation S220 and operation S230.

In operation S340, the measuring device 110 may be configured to comparethe high-resolution image generated in operation S310 with theconversion image provided by operation S330. Based on a result of thecomparison, the measuring device 110 may determine whether to signal tothe first processor executing the image conversion model to againcalibrate the weights and biases of the artificial neural networkthrough the performance of operation S110 to operation S190 of FIG. 2.For example, the measuring device 110 may calculate the MSE as the lossfunction “L” for a difference between the conversion image and thehigh-resolution image.

The measuring device 110 may be configured to repeatedly performoperation S210 to operation S230 when the difference between theconversion image and the high-resolution image (e.g., a value of theloss function “L”) is smaller than or equal to a reference value. Inother exemplary embodiments, the measuring device 110 may performoperation S350 when the difference between the conversion image and thehigh-resolution image is greater than or equal to the reference value.

In operation S350, the measuring device 110 may request the imageconversion model on the first computer 120 to calibrate the weights andbiases of the artificial neural network of the image conversion model.The measuring device 110 may transmit an image pair of thelow-resolution image and the high-resolution image measured in operationS310 to the first computer 120 (this may be similar to operation S120).Here, the image pair may be measured in operation S310 or may be newlygenerated by measuring a new sample semiconductor wafer.

In operation S360, the first processor 121 of the first computer 120 maytransmit the image pair to the second computer 130 for recalibrating theweights and biases of the artificial neural network (this may be similarto operation S140). For example, the first processor 121 may correct anoffset between the low-resolution image and the high-resolution image(this may be similar to operation S130). In other exemplary embodiments,the measuring device 110 may directly request the second computer 130 toagain calibrate the weights and biases of the artificial neural networkof the image conversion model and may directly transmit the image pairof the low-resolution image and the high-resolution image measured inoperation S310 to the second computer 130.

The second processor 131 executing the image conversion model may beconfigured to receive the image pair for re-calibration and mayre-calibrate or tune the weights and biases of the artificial neuralnetwork of the image conversion model by using the image pair. Thesecond processor 131 may be configured to repeatedly perform operationsS150, S151, S152, S153, S160, S170, and S180 described above tore-calibrate the weights and biases of the artificial neural network ofthe image conversion model. The second processor 131 may be configuredto transmit the image conversion model having the trained artificialneural network to the first computer (this may be similar to operationS190). In operation S380, the first computer 120 may store there-calibrated image conversion model to the first memory device 122.

In one exemplary embodiment illustrated in FIG. 11, the operation S340is performed by the measuring device 110. However, in other exemplaryembodiments, operation S340 may be performed by the first processor 121of the first computer 120 executing the image conversion model. In thisembodiment, the measuring device 110 may be configured to transmit boththe low-resolution image and the high-resolution image of the samplesemiconductor wafer to the first computer 120 after performing operationS310. The first processor 121 may convert the low-resolution image byusing the image conversion model. The first processor 121 executing theimage conversion model may be configured to compare the conversion imagewith the high-resolution image. Based on the comparison of theconversion image and the high-resolution image, the measuring device 110may repeatedly perform operation S210 to operation S230 if the imageconversion model is sufficiently accurate. Alternatively, if the imageconversion model is not sufficiently accurate, the second processor 131may be configured to again calibrate the weights and biases of theartificial neural network of the image conversion model.

FIG. 11 is a diagram illustrating a system for monitoring asemiconductor fabrication process according to another embodiment of theinventive concept. A system 200 may include a measuring device 210 and acomputer 220. The measuring device 210 may be identical or similar tothe measuring device 110 described above. For example, the firstsemiconductor wafer WF1 may be a sample semiconductor wafer and thesecond semiconductor wafer WF2 may not be a sample semiconductor wafer.As described above, the measuring device 210 may be provided with aplurality of second semiconductor wafers WF2.

The computer 220 may include a processor 221 and a memory device 222.The computer 220 may be configured to perform all of the above-describedoperations of the first computer 120 and the second computer 130. Theprocessor 221 may be configured to perform all of the above-describedoperations of the first processor 121 and the second processor 131 andthe processor 221 may be implemented with at least one or moreprocessors. The memory device 222 may perform all the above-describedoperations of the first memory device 122 and the second memory device132 and the memory device 222 may be implemented with at least one ormore memory devices. In detail, the first computer 120 and the secondcomputer 130 described above may be integrated into the computer 220.For example, the processor 221 of the computer 220 may performoperations S130 to S190, S230, and S330 to S380.

FIG. 12 is a diagram illustrating a system for monitoring asemiconductor fabrication process according to another embodiment of theinventive concept. A system 300 may include a measuring device 310. Themeasuring device 310 may include the image conversion model and theimage conversion model of the measuring device may perform all of theabove-described operations of the measuring device 110, the firstcomputer 120, and the second computer 130. In this exemplary embodiment,the measuring device 110, the first computer 120, and the secondcomputer 130 may be integrated into the measuring device 310.

In the exemplary embodiment shown in FIG. 12, the measuring device 310may include a first processor 311 similar to the first processor 121described above and a second processor 312 similar to the secondprocessor 131 described above. In other exemplary embodiments, themeasuring device 310 may include a processor into which the firstprocessor 311 and the second processor 312 are integrated. The processormay perform operations S110 to S190, S210 to S230, and S310 to S380.

The measuring device 310 may include a first memory device 313 storingimages of the first semiconductor wafer WF1 and images of the secondsemiconductor wafer WF2, and a second memory device 314 storing an imageconversion model. High-resolution images (e.g., shaded) of the images ofthe first semiconductor wafer WF1 may be generated by measuring thefirst semiconductor wafer WF1. High-resolution images (e.g., shaded) ofthe images of the second semiconductor wafer WF2 may be generated by theimage conversion model. The first memory device 313 and the secondmemory device 314 may be integrated into one memory device.

According to at least one embodiment of the inventive concept, ameasuring device, such as a scanning electron microscope, may quicklygenerate a low-resolution image instead of a high-resolution image. Thelow-resolution image generated by the scanning electron microscope maybe quickly converted to a high-resolution image by using an imageconversion model. Therefore, the scanning electron microscope maymonitor the semiconductor fabrication process in an efficient andeffective manner even if the size of the materials and components of theprocess are very small.

While the inventive concept has been described with reference toexemplary embodiments thereof, it will be apparent to those of ordinaryskill in the art that various changes and modifications may be madethereto without departing from the spirit and scope of the inventiveconcept as set forth in the following claims.

What is claimed is:
 1. A non-transitory computer-readable medium formonitoring a semiconductor fabrication process comprising: an imageconversion model stored on the non-transitory computer-readable medium,the image conversion model having an artificial neural network, whereinthe image conversion model includes instructions executable by at leastone processor, the instructions when executed by the at least oneprocessor, causes the processor to perform: receiving a first image anda second image of a semiconductor wafer, the first image and the secondimage being generated by a measuring device, wherein the second imagehas a higher resolution than the first image; training the artificialneural network by: inputting a dataset representing the first image andthe second image; generating a conversion image of the semiconductorwafer based on the first image, the conversion image having a higherresolution than the first image; calibrating weights and biases of theartificial neural network to match the conversion image to the secondimage within a predetermined differential reference value; andgenerating a third image of the semiconductor wafer based on thecalibrated weights and biases of the artificial neural network.
 2. Thenon-transitory computer-readable medium of claim 1, wherein the firstimage and the second image are measured at the same location of thesemiconductor wafer by the measuring device.
 3. The non-transitorycomputer-readable medium of claim 1, wherein the generation of theconversion image includes: generating first feature map data associatedwith the first image, based on first weights of the weights and firstbiases of the biases; mapping the first feature map data onto secondfeature map data, based on second weights of the weights and secondbiases of the biases; and reconstructing the second feature map data tothe conversion image, based on third weights of the weights and thirdbiases of the biases.
 4. The non-transitory computer-readable medium ofclaim 1, wherein the processor executing the image conversion model isconfigured to compare the conversion image to the second image by usingEquation 1 to determine differences between the conversion image and thesecond image wherein Equation 1 is:${L\left( {W,B} \right)} = {\frac{1}{n}{\sum\limits_{1}^{n}\;{{{C\left( {W,B} \right)} - H}}^{2}}}$wherein, in Equation 1, W is weights of the artificial neural network, Bis biases of the artificial neural network, C is the conversion image, His the second image, n is a number of images received by the processorof the semiconductor wafer, and L is a loss function.
 5. Thenon-transitory computer-readable medium of claim 3, wherein thegenerating of the first feature map data includes performing a firstconvolution operation associated with the first image and the firstweights and a first addition operation associated with a first result ofthe first convolution operation and the first biases, wherein themapping of the first feature map data onto the second feature map dataincludes performing a second convolution operation associated with thefirst feature map data and the second weights and a second additionoperation associated with a second result of the second convolutionoperation and the second biases, and wherein the reconstructing of thesecond feature map data to the conversion image includes performing athird convolution operation associated with the second feature map dataand the third weights and a third addition operation associated with athird result of the third convolution operation and the third biases. 6.The non-transitory computer-readable medium of claim 5, wherein: thefirst convolution operation is performed by using Equation 2; the secondconvolution operation is performed by using Equation 3; and the thirdconvolution operation is performed by using Equation 4 wherein Equation2 is:F ₁(I)=max(0,W ₁ *I+B ₁)<Equation 2> wherein, in Equation 2, F₁(I) isthe first feature map data, W₁ is the first weights, * is a convolutionoperation, I is the first image, and B₁ is the first biases whereinEquation 3 is:F ₂(I)=max(0,W ₂ *F ₁(I)+B ₂  <Equation 3> wherein, in Equation 3, F₂(I)is the second feature map data, W₂ is the second weights, * is aconvolution operation, F₁(I) is the first feature map data, and B₂ isthe second biases wherein Equation 4 is:F ₂(I)=W ₃ *F ₂(I)+B ₃  <Equation 4> wherein, in Equation 4, F₃(I) isthe third feature map data, W₃ is the third weights, * is a convolutionoperation, F₂(I) is the second feature map data, and B₃ is the thirdbiases.
 7. The non-transitory computer-readable medium of claim 1,wherein: the measuring device is a scanning electron microscope; and theartificial neural network is a super resolution convolutional neuralnetwork (SRCNN) including a first layer based on first weights and firstbiases, a second layer based on second weights and second biases, and athird layer based on third weights and third biases.
 8. Thenon-transitory computer-readable medium of claim 1, wherein: theprocessor executing the image conversion model is configured to send acopy of the image conversion model having the trained artificial neuralnetwork to a first device; and the first device is configured togenerate a first high-resolution converted image from a firstlow-resolution image of a second semiconductor wafer.
 9. Thenon-transitory computer-readable medium of claim 8, wherein a seconddevice is configured to: receive the first high-resolution convertedimage from the first device; compare the first high-resolution convertedimage with a high-resolution reference image; and signal to the firstdevice that the artificial neural network of the image conversion modelneeds re-calibrating if differences between the first high-resolutionconverted image and the high-resolution reference image is greater thana predetermined re-calibration differential reference value.
 10. Thenon-transitory computer-readable medium of claim 1, wherein the imageconversion model is further configured to cause the at least oneprocessor to correct an offset between the first image and the secondimage.
 11. The non-transitory computer-readable medium of claim 8,wherein a time necessary for the first device to generate the firsthigh-resolution converted image is less than a time necessary for themeasuring device to generate the second image.
 12. The non-transitorycomputer-readable medium of claim 1, wherein the at least one processoris included in the measuring device.
 13. A method of converting an imageof a semiconductor wafer to monitor a semiconductor fabrication process,the method comprising: receiving a first image and a second image of asemiconductor wafer by a processor executing an image conversion modelhaving an artificial neural network; training the artificial neuralnetwork of the image conversion model by: inputting a datasetrepresenting the first image and the second image; generating aconversion image of the semiconductor wafer based on the first image,the conversion image having a higher resolution than the first image;calibrating weights and biases of the artificial neural network to matchthe conversion image to the second image within a predetermineddifferential reference value; and generating a third image based on thecalibrated weights and biases of the artificial neural network.
 14. Themethod of claim 13, wherein the generation of the conversion imageincludes: generating first feature map data associated with the firstimage, based on first weights of the weights and first biases of thebiases; mapping the first feature map data onto second feature map data,based on second weights of the weights and second biases of the biases;and reconstructing the second feature map data to the conversion image,based on third weights of the weights and third biases of the biases.15. The method of claim 14, wherein the generating of the first featuremap data includes performing a first convolution operation associatedwith the first image and the first weights and a first additionoperation associated with a first result of the first convolutionoperation and the first biases, wherein the mapping of the first featuremap data onto the second feature map data includes performing a secondconvolution operation associated with the first feature map data and thesecond weights and a second addition operation associated with a secondresult of the second convolution operation and the second biases, andwherein the reconstructing of the second feature map data to theconversion image includes performing a third convolution operationassociated with the second feature map data and the third weights and athird addition operation associated with a third result of the thirdconvolution operation and the third biases.
 16. The method of claim 15,wherein: the first convolution operation is performed by using Equation2; the second convolution operation is performed by using Equation 3;and the third convolution operation is performed by using Equation 4wherein Equation 2 is:F ₁(I)=max(0,W ₁ *I+B ₁)  <Equation 2> wherein, in Equation 2, F₁(I) isthe first feature map data, W₁ is the first weights, * is a convolutionoperation, I is the first image, and B₁ is the first biases whereinEquation 3 is:F ₂(I)=max(0,W ₂ *F ₁(I)+B ₂)  <Equation 3:> wherein, in Equation 3,F₂(I) is the second feature map data, W₂ is the second weights, * is aconvolution operation, F₁(I) is the first feature map data, and B₂ isthe second biases wherein Equation 4 is:F ₃(I)=W ₃ *F ₂(I)+B ₃  <Equation 4> wherein, in Equation 4, F₃(I) isthe third feature map data, W₃ is the third weights, * is a convolutionoperation, F₂(I) is the second feature map data, and B₃ is the thirdbiases.
 17. The method of claim 13, further comprising: transmitting acopy of the image conversion model having the trained artificial neuralnetwork to a first device; and generating a first high-resolutionconverted image from a dataset of a first low-resolution image of asecond semiconductor wafer by the first device.
 18. A system comprising:at least one processor; and at least one non-transitorycomputer-readable storage medium storing instructions that, whenexecuted by the at least one processor, cause the system to: receive afirst image and a second image of a semiconductor wafer, the first imageand the second image being generated by a scanning electron microscope,wherein the second image has a higher resolution than the first image;train an artificial neural network of an image conversion model by:inputting a dataset representing the first image and the second image;generate a conversion image of the semiconductor wafer based on thefirst image, the conversion image having a higher resolution than thefirst image; calibrating weights and biases of the artificial neuralnetwork to match the conversion image to the second image within apredetermined differential reference value; and generating a third imageof the semiconductor wafer based on the calibrated weights and biases ofthe artificial neural network.
 19. The system of claim 18, wherein thegeneration of the conversion image includes: generating first featuremap data associated with the first image, based on first weights of theweights and first biases of the biases; mapping the first feature mapdata onto second feature map data, based on second weights of theweights and second biases of the biases; and reconstructing the secondfeature map data to the conversion image, based on third weights of theweights and third biases of the biases.
 20. The system of claim 19,wherein the generating of the first feature map data includes performinga first convolution operation associated with the first image and thefirst weights and a first addition operation associated with a firstresult of the first convolution operation and the first biases, whereinthe mapping of the first feature map data onto the second feature mapdata includes performing a second convolution operation associated withthe first feature map data and the second weights and a second additionoperation associated with a second result of the second convolutionoperation and the second biases, and wherein the reconstructing of thesecond feature map data to the conversion image includes performing athird convolution operation associated with the second feature map dataand the third weights and a third addition operation associated with athird result of the third convolution operation and the third biases.